Answers
1 Yes. We can toss a ball straight up. If it is deflected, we know we are in motion relative to the water.
2 No. The principle of relativity applies.
3 Yes. We can throw a stone into the water. If the ship moves with respect to the point from which the circular wavefronts emanate, then we are in motion relative to the water.
4 Yes. We can get a friend to fly over us in an airplane. If he sees we are moving, then we are in motion relative to the water.